Analog circuits often use amplifiers such as op amps to amplify a signal. Signals may have a dynamic range that is better expressed using a logarithmic scale rather than a linear scale. A ratio of one signal to another is often expressed in Decibels (dB) to show the exponential term rather than the linear values. For example, a signal-to-noise ratio is commonly expressed in dB.
Since signal intensity or power is often caused by exponential physical responses of silicon junctions and other structures, electronic circuits that operate logarithmically rather than linearly are sometimes desired. For example, a security system may have a signal-to-jammer ratio where the jammer power is programmable in logarithmic steps, rather than in linear steps. Some measurement systems that provide time gain compensation, such as ultrasound measurement in the medical field, or radar systems, or various communications systems with automatic gain control, can benefit from logarithmically-programmable amplifiers.
FIGS. 1A-B show gain amplifiers. In FIG. 1A, amplifier 10 compares voltages on its inverting (−) and non-inverting (+) inputs to drive an output VOUT. Feedback resistor 14 is connected between VOUT and the inverting input. The non-inverting (+) inputs to amplifier 10 is grounded. Series resistor 12 is connected between input VIN and the inverting input at node VS. The output voltage VOUT is equal to VIN multiplied by −1*RF/RS, where RF is the resistance value of feedback resistor 14 and RS is the resistance value of series resistor 12. This circuit configuration is inverting, since the polarity of changes in VIN are inverted to VOUT. The gain or amplification can be set to a desired value by selecting values of RS and RF.
In FIG. 1B, VIN is applied directly to the non-inverting (+) input to amplifier 10. Series resistor 12 is connected between ground and the inverting input at node VS. The output voltage VOUT is equal to VIN multiplied by [1+(RF/RS)]. This circuit configuration is non-inverting, since the polarity of changes in VIN are not inverted to VOUT. Amplifier 10 adjusts VOUT until its inputs VS and VIN are equal in voltage. Selecting values of RS and RF allow a desired gain to be achieved.
Systems with automatic gain control or gain compensation may use a variable-gain amplifier. The gain of the amplifier is changed during operation, such as by stepping up the gain in increments until an output is within a desired range. Each change in an input signal can result in the gain being stepped up or down to compensate.
The gain can be adjusted by changing the resistance values RS or RF. FIG. 2 shows a programmable gain amplifier circuit that has selectable resistors in parallel on the input. Input VIN is buffered by driver 16 to drive one terminal of each of series resistors 22. Switches 20 are transmission gates that connect the other terminal of one or more of series resistors 22 to node VS, the inverting input of amplifier 10. The non-inverting input is grounded. Feedback resistor 14 is connected between VS and VOUT.
The gain is −RS/RF, where RS is now variable and depends on which of series resistors 22 are connected by switches 20. As more of series resistors 22, or lower resistance values of series resistors 22 are selected by switches 20, RS decreases and the magnitude of the gain increases.
FIG. 3 is a table of resistor values to produce logarithmic gain increments. While the resistance values of series resistors 22 (FIG. 2) could be set to the same value, the increments of overall RS achieved would not be logarithmic. Specific values of series resistors 22 are needed to provide logarithmic increments in RS and gain. A three-bit control word CTRL can control 8 switches 20 to select from among 8 series resistors 22. Each of the 8 series resistors 22 has a different resistance value, as shown in the last column of the table.
The gain increases by 2 Decibels for each increment in control word CTRL. However, the linear gain values 1.00, 1.259, 1.585, 1.995, . . . require precise resistor values for series resistors 22 of 10, 7.943, 6.31, 5.102, . . . Kohm when feedback resistor 14 has a 10-Kohm value.
Each of the eight values of series resistors 22 is different and must be precisely matched to each other and to the 10-Kohm value of feedback resistor 14. There are no common factors or ratios to simplify this resistor-matching problem. A total of 9 resistors, all with different values, must be precisely matched to achieve precise logarithmic steps.
Resistor matching is sometimes achieved by careful placement and layout of resistors on an Integrated Circuit (IC). Such careful layout is difficult and potentially expensive. Slight offsets of lithographic equipment may add resistances in one direction and not in another, such as when contacts are mis-aligned to a substrate resistor diffusion.
As the number of logarithmic steps increases, so does the number of resistors that have to be matched to one another. The number of resistor ratios than need to be matched is proportional to 2N, where N is the number of bits in control word CTRL. Thus scaling the variable-gain amplifier of FIG. 2 to greater programmability is problematic due to this resistor-matching problem.
FIG. 4 shows a variable-gain amplifier circuits using series resistors 22 in series. Buffer 16 buffers VIN and drives the first of a series of series resistors 22 in a chain of series resistors 22 to the inverting input of amplifier 10. Switches 20 close to bypass one or more of series resistors 22, reducing the overall resistance RS and thus increasing the gain's magnitude.
This series arrangement of series resistors 22 also suffers from the resistor-ratio matching problem, since there are no common factors in the resistance values of FIG. 3, so 10 resistors need to be matched for a 3-bit control word CTRL.
The series arrangement also suffers from another problem caused by switches 20. In the parallel arrangement of FIG. 2, node VS is driven to ground by amplifier 10. Thus one terminal of each of switches 10 is connected to a virtual ground. However, in the series arrangement of FIG. 4, the terminals of most of switches 10 are at voltages that are not virtual ground. The magnitudes of the threshold voltages of MOS transistors increase when their sources are floating. The larger thresholds can turn off the MOS transistors, or cause the transistors to operate in the saturated region rather than in the linear region.
FIGS. 5A-B highlight the MOS transistor switch problem at low power-supply voltages. In FIG. 5A, the power supply voltage VDD is larger than the sum of the n-channel MOS transistor threshold voltage Vtn and the absolute value of the p-channel MOS transistor threshold voltage |Vtp|.
In FIG. 5B, VDD has a lower value so that VDD is less than Vtn+|Vtp|. A transmission gate switch such as switches 20 cannot always fully open and fully close to select and isolate series resistors 22. Current leakage can occur when switches 20 should be turned off. Power-supply voltages of 3.3 volts to as low as 1.0 volt are needed for more advanced semiconductor processes that use very short gate lengths, such as 350 nm to as low as 40 nm.
What is desired is a Programmable-Gain Amplifier (PGA) that has logarithmic steps. A PGA with logarithmic-in-Decibel steps is desired that can be used for either inverting or non-inverting configurations. A PGA that avoids both the resistor-matching problem and the MOS transistor switch problem is desired. A PGA that uses only a few resistor values yet has many programmable steps is desired. A logarithmic-in-dB PGA using only 3 resistor values for 8 or more logarithmic steps with MOS switches that are connected to a virtual ground is desired. A differential PGA is also desired with many logarithmic steps and few resistance values to match, and without floating MOS switches.